Study On Dynamic Modulus Of Bioinspired Composites With Floquet-based Bar-spring Model

Typical load-bearing biological materials such as nacre,bone and tooth,all have extraordinary mechanical properties significantly surpassing those of artificial composites.It is of great importance to figure out the “microstructure-mechanical property” relationship and unveil the underlying principles of design for developing high-performance bioinspired composites.Currently,most of the existing researches characterizing the microstructure-property relationships of biological and bioinspired composites have two major drawbacks.Firstly,the theoretical models usually make many simplifications and assumptions and are only applicable to a few regular microstructures with unitary reinforcements uniformly distributed,and consequently limit their applications to the biological/bioinspired composites in reality whose microstructures are quite diverse and complex.Secondly,most of these researches are just focused on the static mechanical property,while the daily and fatal loadings on real biological materials are usually dynamic like blast,shock wave and so forth.In order to overcome these drawbacks,using Floquet theory we developed a generic FloquetBased Bar-Spring(FBBS)model to predict the dynamic modulus of biological and bioinspired composites with arbitrary staggered microstructures.In order to verify the model,the finite element simulations were also conducted via ABAQUS to obtain the dynamic modulus for several typical microstructures widely seen in load-bearing biological materials.Comparisons between the theoretical predictions and FEM results show that FBBS model is more accurate than the previous Tension-Shear Chain(TSC)models.Then the influences of several structural and materials factors on the dynamic modulus of composites are evaluated using FBBS model.The major findings and conclusions are summarized as below:(1)for any given specific aspect ratio,as the loading frequency increases,the storage modulus of microstructured composites gradually approaches to a upper bound,while the loss modulus demonstrates a peak value at the optimal working frequency;(2)as the aspect ratio of hard reinforcements increases,the storage modulus of biological structures always increases,but the varying of loss modulus depends on the constituent material properties;(3)elastic modulus mismatch between hard and soft components seems beneficial to the composites damping property,so does the offset parameter of the regular staggered structure;(4)the characteristic relaxation time of matrix material mainly influences the optimal working frequency,while the viscoelastic coefficients mainly affect the peak value of loss modulus.The model and studies here are not only important for understanding the “microstructure-mechanical property” relationship in load-bearing biological materials,but also provided useful guidelines for the design of high performance bioinspired composites.